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CPET 190
User Defined Functions
Lecture 12
Problem Solving with MATLAB
http://www.etcs.ipfw.edu/~lin
November 1, 2005
Lecture 12 - By Paul Lin
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User-Defined M-File Functions
12-1 Intro to MATLAB Functions
12-2 Variable Passing (By Value)
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Lecture 12 - By Paul Lin
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User-Defined M-File Functions
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Past 30-years Programming Practices
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Reuse
Portability
Reliability
Maintainability
Programming Language and Practices
• Modular (Structured) Programming (1970 to late
1980s) – Fortran, C, Ada; (MATLAB 1990 – present)
• Object-Oriented Programming (1990s) – SmallTalk,
C++, Java
• Component-Based Programming (2000s) – C#, or
.NET
November 1, 2005
Lecture 12 - By Paul Lin
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User-Defined M-File Functions
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MATLAB Programming Language Features
(Modular and Structured)
• Top-down design – Module and subtasks
• Independent testing of function-level sub-tasks maintainability
• Reuse – reusability thorough packaging of
functions , reduce programming efforts and
increasing productivity
• Isolation from unintended side effects – reliability
through data hiding, separate workspace for each
function to avoid certain mistakes
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Lecture 12 - By Paul Lin
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Introduction to MATLAB
Functions
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Types of M-File Functions
• MATLAB Built-In
Functions: abs(x), cos(x),
sin(x), max(x)
• User-Defined M-File
Functions (increase code
re-usability)
Functions
• Subroutines or
Procedures (providing
services)
• Function name,
arguments, return
arguments list (values)
• Function Calls
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Lecture 12 - By Paul Lin
Input Data
Function
M File
Output Data
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Introduction to MATLAB
Functions
MATLAB Function Format
function [out_arg1, out_arg2, …] =
function_name(in_arg1, in_arg2, …)
% Comments lines
% More comments
Executable codes
(return)
-- Optional
(end)
-- For version 7.0 and newer
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Lecture 12 - By Paul Lin
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MATLAB Built-In Functions
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Toolbox\matlab\
• elefun folder
(elementary functions)
• elemat folder
(elementary matrix
function)
• general folder
• etc
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Lecture 12 - By Paul Lin
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MATLAB Built-In Functions
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\toolbox\matlab\elefun
Elementary Math
Functions
• abs.m
• exp.m
• cos.m
• sin.m
• pow.m
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Lecture 12 - By Paul Lin
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MATLAB fliplr Function
function y = fliplr(x)
%FLIPLR Flip matrix in left/right direction.
% FLIPLR(X) returns X with row preserved and columns flipped
% in the left/right direction.
%
8-line Help Comments
% X = 1 2 3 becomes 3 2 1
%
456
654
An Example
%
% See also FLIPUD, ROT90, FLIPDIM.
% Copyright 1984-2002 The MathWorks, Inc.
% $Revision: 5.9 $ $Date: 2002/04/08 20:21:05 $
if ndims(x)~=2, error('X must be a 2-D matrix.'); end
[m,n] = size(x);
y = x(:,n:-1:1);
Error Checking
Return value
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Lecture 12 - By Paul Lin
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fliplr Function
If x = [1 2 3; 4 5 6]; or
=1 2 3
45 6
[m,n] = size(x)
m= 2, n = 3
y = x(:,n:-1:1);
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x(:,
-- All rows remain unchanged
n:-1:1 -- Colon operator to access column elements
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The meaning of first n is to copy the column-n of the x array, into
the column-1 of the y array
The meaning of the :1 is to copy the column 1 of x into the very
last column of y
The meaning of the :-1 is to copy column n-1 of x into column n-1
of y; then decrement the column by -1 to copy the column n-2 of x
into the column-2 of y; until all columns between n and 1 are
copied.
y=3 2 1
6 5 4
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Lecture 12 - By Paul Lin
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View fliplr Function
>> dbtype fliplr
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function y = fliplr(x)
%FLIPLR Flip matrix in left/right direction.
% FLIPLR(X) returns X with row preserved and columns flipped
% in the left/right direction.
%
% X = 1 2 3 becomes 3 2 1
%
456
654
%
% See also FLIPUD, ROT90, FLIPDIM.
% Copyright 1984-2002 The MathWorks, Inc.
% $Revision: 5.9 $ $Date: 2002/04/08 20:21:05 $
if ndims(x)~=2, error('X must be a 2-D matrix.'); end
[m,n] = size(x);
y = x(:,n:-1:1);
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Example 1 A User-Define Function
Example
Phases of Function Development
Designing phase
Coding phase
Testing Phase
Release and Implementation
The Desired Function
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Calculating the Hypotenuse
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Hypotenuse – the side of a righttriangle that is opposite the right
angle (domain knowledge)
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Function name – hypotenuse
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Input arguments – a, b
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Output arguments – h
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The function hypotenuse.m
function h = hypotenuse(a, b)
h = sqrt(a.^2 + b.^2);
November 1, 2005
A
h
C
a
b
B
AC - Hypotenuse
Lecture 12 - By Paul Lin
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Example 1 A User-Define Function
Example
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Code the hyotense.m M-file function and save it under
cpet190/codes folder
Run the function: Click on Debug -> Run
Error message shows
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Lecture 12 - By Paul Lin
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Example 1 A User-Define Function
Example
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Testing Functions:
First Testing:
hypotense(3,4)
Second Testing:
a = 3, b =4;
hypotenuse(a,b)
Third Testing:
side_a = 3; side_b = 4;
c = hypotenuse(side_a,
side_b)
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Lecture 12 - By Paul Lin
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Variable Passing (By Value)
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MATLAB programs communicate with their
functions – values passing for both arrays
and scalars
Make a copy of the actual arguments and
passes them to the function
Service requesting function cannot modify
the actual arguments
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Lecture 12 - By Paul Lin
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Example 2 Parallel Resistance
Function for calculating Parallel
resistance
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Domain Knowledge:
Req = R1 || R2 = (R1 * R2)/(R1 + R2)
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Function design
function Req = p_rs(r1, r2)
% Comments
%
if r1 < 0
Req = -1;
elseif r2 < 0
Req = -1;
elseif (r1 == 0) || (r2 == 0)
Req = 0;
else
Req = (r1 * r2)/(r1 + r2)
end
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November 1, 2005
Lecture 12 - By Paul Lin
R1
R2
Rn
RT = xxx Ω
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Example 2 Parallel Resistance
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Coding
Documentation
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Purposes
Calling sequence
Defining Variables
Record of revisions
Testing
• p_rs(10,10) -- 5 ohms
• p_rs(10, p_rs(20,20)) – 5
ohms
• p_rs(ra, rb)
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Lecture 12 - By Paul Lin
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Example 3 Rectangular-to-Polar
Conversion
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Problem Statement
• The location of a point
in a cartesian plane can
be expressed in either
the rectangular
coordinates(x,y) or the
polar coordinates(r,
theta) as shown on the
slide.
• The point P(x,y) or P(r,
theta)
• Two functions for
converting between
rectangular coordinate
polar coordinate
November 1, 2005
Lecture 12 - By Paul Lin
Y Axis
P
y
r
q
x
X Axis
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Example 3 Rectangular-to-Polar
Conversion
Domain Knowledge
x = r cos(theta)
y= r sin(theta)
r = sqrt(x^2 + y^2)
theta = tan-1(y/x)
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Define the function’s name, inputs and outputs
function [x, y] polar2rect(r, theta)
function [r, theta] rect2polar(x,y)
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Convert equations to MATLAB statement
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Code and test function
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Add documentation to the two functions
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November 1, 2005
Lecture 12 - By Paul Lin
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Example 3 Rectangular-to-Polar
Conversion
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The two functions
function [x, y] = polar2rect(r, theta)
x = r * cos(theta*pi/180);
y = r * sin(theta*pi/180);
end
November 1, 2005
Lecture 12 - By Paul Lin
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Example 3 Rectangular-to-Polar
Conversion
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The two functions
function [r, theta] = rect2polar(x,y)
%ATAN2 Four quadrant inverse tangent.
% ATAN2(Y,X) is the four quadrant arctangent
of the
% real parts of the elements of X and Y.
% -pi <= ATAN2(Y,X) <= pi.
r = sqrt(x^2 + y^2);
theta = (180/pi)* atan2(y,x);
end
November 1, 2005
Lecture 12 - By Paul Lin
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Example 3 Rectangular-to-Polar
Conversion
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Testing Functions
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Testing Functions
>> [r, theta] = rect2polar(4,3)
r=
5
theta =
36.8699
>> [x, y] = polar2rect(5, 36.8699)
x=
4.0000
y=
3.0000
>> [r, theta] = rect2polar(-4,-3)
r=
5
theta =
-143.1301
>> [x, y] = polar2rect(5, -36.8699)
x=
4.0000
y=
-3.0000
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Lecture 12 - By Paul Lin
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Summary
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Intro to MATLAB Functions
Variable Passing (By Value)
Example 1 – Function for Hypotenuse
calculation
Example 2 – Function for Parallel
Resistance computation
Example 3 – Function for rectangular to
polar conversion
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Lecture 12 - By Paul Lin
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